Bubbles and Drops on Curved Surfaces

Surface curvature affects the shape, stability, and apparent contact angle of sessile and pendant drops. Here, we develop an approximate analytical solution for non-axisymmetric perturbations to small spherical drops on a flat substrate, assuming a fixed contact angle and fixed drop volume. The analytical model is validated using numerical solutions of the Laplace equation from the Surface Evolver software. We investigate the effects of surface curvature on drop shape, pressure, and surface energy, ascertaining the energy-gradient force that drives lateral drop migration. By balancing this force with the viscous resistance/drag force, in the lubrication approximation, we predict velocities of the order of 0.1 mm s–1 for 1 mm diameter drops of water with a 30° contact angle on a substrate with a curvature gradient of 0.01 mm–2, achieved, for example, on a harmonic surface with a wavelength of 4 cm and an amplitude of 4 mm.